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# Ch010 - Chapter 10 Return and Risk The...

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Chapter 10: Return and Risk: The Capital-Asset-Pricing Model (CAPM) 10.1 a. Expected Return = (0.1)(-0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207) = 0.1057 = 10.57% The expected return on Q-mart’s stock is 10.57%. b. Variance ( σ 2 ) = (0.1)(-0.045 – 0.1057) 2 + (0.2)(0.044 – 0.1057) 2 + (0.5)(0.12 – 0.1057) 2 + (0.2)(0.207 – 0.1057) 2 = 0.005187 Standard Deviation ( σ ) = (0.005187) 1/2 = 0.0720 = 7.20% The standard deviation of Q-mart’s returns is 7.20%. 10.2 a. Expected Return A = (1/3)(0.063) + (1/3)(0.105) + (1/3)(0.156) = 0.1080 = 10.80% The expected return on Stock A is 10.80%. Expected Return B = (1/3)(-0.037) + (1/3)(0.064) + (1/3)(0.253) = 0.933 = 9.33% The expected return on Stock B is 9.33%. b. Variance A ( σ A 2 ) = (1/3)(0.063 – 0.108) 2 + (1/3)(0.105 – 0.108) 2 + (1/3)(0.156 – 0.108) 2 = 0.001446 Standard Deviation A ( σ A ) = (0.001446) 1/2 = 0.0380 = 3.80% The standard deviation of Stock A’s returns is 3.80%. Variance B ( σ B 2 ) = (1/3)(-0.037 – 0.0933) 2 + (1/3)(0.064 – 0.0933) 2 + (1/3)(0.253 – 0.0933) 2 = 0.014447 Standard Deviation B ( σ B )= (0.014447) 1/2 = 0.1202 = 12.02% The standard deviation of Stock B’s returns is 12.02%. c. Covariance(R A , R B ) = (1/3)(0.063 – 0.108)(-0.037 – 0.0933) + (1/3)(0.105 – 0.108)(0.064 – 0.933) + (1/3)(0.156 – 0.108)(0.253 – 0.0933) = 0.004539 The covariance between the returns of Stock A and Stock B is 0.004539. B-190

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Correlation(R A ,R B ) = Covariance(R A , R B ) / ( σ A * σ B ) = 0.004539 / (0.0380 * 0.1202) = 0.9937 The correlation between the returns on Stock A and Stock B is 0.9937. 10.3 a. Expected Return HB = (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154) = 0.0733 = 7.33% The expected return on Highbull’s stock is 7.33%. Expected Return SB = (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074) = 0.0608 = 6.08% The expected return on Slowbear’s stock is 6.08%. b. Variance A ( σ HB 2 ) = (0.25)(-0.02 – 0.0733) 2 + (0.60)(0.092 – 0.0733) 2 + (0.15)(0.154 – 0.0733) 2 = 0.003363 Standard Deviation A ( σ HB ) = (0.003363) 1/2 = 0.0580 = 5.80% The standard deviation of Highbear’s stock returns is 5.80%. Variance B ( σ SB 2 ) = (0.25)(0.05 – 0.0608) 2 + (0.60)(0.062 – 0.0608) 2 + (0.15)(0.074 – 0.0608) 2 = 0.000056 Standard Deviation B ( σ B )= (0.000056) 1/2 = 0.0075 = 0.75% The standard deviation of Slowbear’s stock returns is 0.75%. c. Covariance(R HB , R SB ) = (0.25)(-0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 – 0.0733)(0.062 – (0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608) = 0.000425 The covariance between the returns on Highbull’s stock and Slowbear’s stock is 0.000425. Correlation(R A ,R B ) = Covariance(R A , R B ) / ( σ A * σ B ) = 0.000425 / (0.0580 * 0.0075) = 0.9770 The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770. B-192

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10.4 Value of Atlas stock in the portfolio = (120 shares)(\$50 per share) = \$6,000 Value of Babcock stock in the portfolio = (150 shares)(\$20 per share) = \$3,000 Total Value in the portfolio = \$6,000 + \$3000 = \$9,000 Weight of Atlas stock = \$6,000 / \$9,000 = 2/3 The weight of Atlas stock in the portfolio is 2/3. Weight of Babcock stock = \$3,000 / \$9,000 = 1/3 The weight of Babcock stock in the portfolio is 1/3. 10.5 a. The expected return on the portfolio equals: E(R P ) = (W F )[E(R F )] + (W G )[E(R G )] where E(R P ) = the expected return on the portfolio E(R F ) = the expected return on Security F E(R G ) = the expected return on Security G W F = the weight of Security F in the portfolio W G = the weight of Security G in the portfolio E(R P ) = (W F )[E(R F )] + (W G )[E(R G )] = (0.30)(0.12) + (0.70)(0.18) = 0.1620 = 16.20% The expected return on a portfolio composed of 30% of Security F and 70% of Security G is 16.20%. b. The variance of the portfolio equals: σ 2 P = (W F ) 2 ( σ F ) 2 + (W G ) 2 ( σ G ) 2 + (2)(W F )(W G )( σ F )( σ G )[Correlation(R F , R G )] where σ 2 P = the variance of the portfolio W F = the weight of Security F in the portfolio W G = the weight of Security G in portfolio σ F = the standard deviation of Security F σ G = the standard deviation of Security G R F = the return on Security F R G = the return on Security G σ 2 P = (W F ) 2 ( σ F ) 2 + (W G ) 2 ( σ G ) 2 + (2)(W F )(W G )( σ F )( σ G
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Ch010 - Chapter 10 Return and Risk The...

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